基于图解静力法的桁架优化程序开发及应用
摘要：介绍了图解静力学和绘制桁架轴力线图的方法，基于面向对象方法编写绘制桁架结构轴力线图的优化程序，为了得到稳定的轴力线图，采用基于杆系有限元方法先计算轴力，再通过拓扑关系绘制轴力线图。在计算过程中计算并实时显示虚功代表值，有利于工程师通过调整桁架形状实时进行找形优化。结合算例描述基于图解静力法对桁架进行结构优化的计算过程。最后通过一个工程算例展示基于图解静力法对桁架结构进行优化的有效性。
关键词：钢桁架结构；图解静力法；结构优化；优化程序
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参考文献[1] ZILLICH K,STIEGLER F.Graphische statik[M].Zurich:Verlag Von Meyer & Zeller,1866.
[2] BOJCZUK D,MRÓZ Z.Optimal topology and configuration design of trusses with stress and buckling constraints [J].Structural Optimization,1999,17(1):25-35.
[3] MAZUREK A.Geometrical aspects of optimum truss like structures for three-force problem [J].Structural and Multidisciplinary Optimization,2012,45(1):21-32.
[4] BAKER W F,BEGHINI L L,MAZUREK A,et al.Maxwell’s reciprocal diagrams and discrete Michell frames[J].Structural and Multidisciplinary Optimization,2013,48(2):267-277.
[5] STROMBERG L L,BEGHINI A,BAKER W F,et al.Topology optimization for braced frames:combining continuum and beam/column elements[J].Engineering Structures,2012,37:106-124.
[6] BENDSØE M P,SIGMUND O.Material interpolation schemes in topology optimization [J].Archive of Applied Mechanics,1999,69(9-10):635-654.
[7] TYAS A,PICHUGIN A V,GILBERT M.Optimum structure to carry a uniform load between pinned supports:exact analytical solution [J].Proceedings of the Royal Society A:Mathematical,Physical and Engineering Sciences,2011,467(2128):1101-1120.
[8] 曾浩杰.图解静力学在建筑形态创作中的应用研究[D].成都：西南交通大学，2019.
[9] ZASTAVNI D.The structural design of Maillart’s chiasso shed (1924):a graphic procedure [J].Structural Engineering International,2008,18(3):247-252.
[10] BEGHINI L,CARRION J,BEGHINI A,et al.Structural optimization using graphic statics [J].Structural and Multidisciplinary Optimization,2014,49(3):351-366.
[11] 赵洁，马思嘉，乔文涛，等.基于图解静力学的平面桁架形态设计方法研究[J].建筑科学，2019,35(7):53-58.
[12] ZHOU M,ROZVANY G.The COC algorithm,part II:Topological,geometrical and generalized shape optimization[J].Computer Methods in Applied Mechanics and Engineering,1991,89(1-3):309-336.
[2] BOJCZUK D,MRÓZ Z.Optimal topology and configuration design of trusses with stress and buckling constraints [J].Structural Optimization,1999,17(1):25-35.
[3] MAZUREK A.Geometrical aspects of optimum truss like structures for three-force problem [J].Structural and Multidisciplinary Optimization,2012,45(1):21-32.
[4] BAKER W F,BEGHINI L L,MAZUREK A,et al.Maxwell’s reciprocal diagrams and discrete Michell frames[J].Structural and Multidisciplinary Optimization,2013,48(2):267-277.
[5] STROMBERG L L,BEGHINI A,BAKER W F,et al.Topology optimization for braced frames:combining continuum and beam/column elements[J].Engineering Structures,2012,37:106-124.
[6] BENDSØE M P,SIGMUND O.Material interpolation schemes in topology optimization [J].Archive of Applied Mechanics,1999,69(9-10):635-654.
[7] TYAS A,PICHUGIN A V,GILBERT M.Optimum structure to carry a uniform load between pinned supports:exact analytical solution [J].Proceedings of the Royal Society A:Mathematical,Physical and Engineering Sciences,2011,467(2128):1101-1120.
[8] 曾浩杰.图解静力学在建筑形态创作中的应用研究[D].成都：西南交通大学，2019.
[9] ZASTAVNI D.The structural design of Maillart’s chiasso shed (1924):a graphic procedure [J].Structural Engineering International,2008,18(3):247-252.
[10] BEGHINI L,CARRION J,BEGHINI A,et al.Structural optimization using graphic statics [J].Structural and Multidisciplinary Optimization,2014,49(3):351-366.
[11] 赵洁，马思嘉，乔文涛，等.基于图解静力学的平面桁架形态设计方法研究[J].建筑科学，2019,35(7):53-58.
[12] ZHOU M,ROZVANY G.The COC algorithm,part II:Topological,geometrical and generalized shape optimization[J].Computer Methods in Applied Mechanics and Engineering,1991,89(1-3):309-336.
Development and application of a truss structure optimization program based on graphic statics
Abstract: Graphic statics and a method of drawing axial force diagram of truss was introduced; the optimization program to draw axial force diagram of truss structure was developed based on an object-oriented method. To obtain stable axial force diagram, axial force was calculated firstly using finite element method based on bar system, and axial force diagram was drawn through topological relations. Virtual work representative value was calculated and displayed in real time in program calculation, which allows engineers to optimize the truss shape in real time. A calculation example was shown to demonstrate the calculation procedure of truss structure optimization based on graphic statics. Finally, an analysis of engineering example was used to exhibit the effectiveness of truss structure optimization based on graphic statics.
Keywords: steel truss structure; graphic statics; structure optimization; optimization program
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